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SUMMARY:On the moduli space of log K-polystable pairs formed by a hypersur
 face and a hyperplane section. - Jesus Martinez-Garcia (Max Planck)
DTSTART:20170201T141500Z
DTEND:20170201T151500Z
UID:TALK69533@talks.cam.ac.uk
CONTACT:Dr. J Ross
DESCRIPTION:We study compactifications log pairs (X\,D) where X is a hyper
 surface in projective space of some fixed degree and D is a hyperplane sec
 tion. Geometric Invariant Theory is known to provide a finite number of po
 ssible compactifications of such pairs\, depending on one parameter. Any t
 wo such compactifications are related by birational transformations. We de
 scribe an algorithm to study the stability of these pairs\, and apply our 
 algorithm to the case of cubic surfaces. Finally\, we relate this compacti
 fications to the moduli space of pairs (X\,D) where X admits a Kaehler-Ein
 stein metric with singularities along D. We show that any such pair is an 
 element of our moduli and that there is a naturally defined line bundle co
 ming from the geometry which polarizes our compactifications.\nThis is an 
 (ongoing) joint project with Patricio Gallardo (University of Georgia) and
  Cristiano Spotti (Aarhus University).\n\n
LOCATION:CMS MR13
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